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The equation of a parabola is y=x2−6x+18y = x^2 - 6x + 18. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______

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Q. The equation of a parabola is y=x2−6x+18y = x^2 - 6x + 18. Write the equation in vertex form.\newlineWrite any numbers as integers or simplified proper or improper fractions.\newline______
  1. Identify Vertex Form: Identify the vertex form of a parabola. Vertex form is y=a(x−h)2+ky = a(x - h)^2 + k.
  2. Complete Square: Complete the square for the equation y=x2−6x+18y = x^2 - 6x + 18.\newlineHalf of the linear coefficient is −62=−3-\frac{6}{2} = -3.\newlineSquare it to get (−3)2=9(-3)^2 = 9.
  3. Add and Subtract: Add and subtract the squared term inside the equation. y=x2−6x+9+18−9y = x^2 - 6x + 9 + 18 - 9.
  4. Group Trinomial and Constants: Group the perfect square trinomial and the constants.\newliney=(x2−6x+9)+(18−9)y = (x^2 - 6x + 9) + (18 - 9).
  5. Factor Perfect Square Trinomial: Factor the perfect square trinomial. y=(x−3)2+9y = (x - 3)^2 + 9.
  6. Combine Constants: Combine the constants.\newliney=(x−3)2+9y = (x - 3)^2 + 9.

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